so we set it equal to zero, then less than for negative, then greater than for positive. Ok.
Let's start with setting it equal to zero. Do not distribute, leave the equation as is. Go to each ( ) and think what will x need to be to make this zero. Only one needs to be zero for the whole thing to be zero. There should be 3 answers. I'll give you a sec.
Let me know if you didn't understand what I just said

But here is where it is tricky. Say we use the number 0 which satisfies the first but not the last two. Lets see if we get a positive number.
0<(0-7)(3(0)+1)(0+4)
0<-7*1*4
0<-28
no.
So the answer for 0<.... is x<-4
because that is the lowest.
***I missed typed above this is for the positive****

How to solve problems like this.
Set equal to zero. Solve each term for the zeros.
Put those points on a number line. Pick easy numbers between those points. Test to see if it is positive or negative.
Follow the number line like a map to get the solutions for neg and pos.

Sorry for leading you estray but sometimes working through a problem and finding mistakes helps us understand a little more about the correct way in terms of what is not right.
I think a sign graph is very helpful, I'd continue to use that.
Do you think you could do a problem like this by yourself now?
Thanks for refreshing me as well. It took a while but we got it !!